Low Frequency Hierarchical Cooperative Impulse Control for Gravitational Wave Detector Formation Keeping

Abstract

Configuration stability is crucial for the detection accuracy of space-based gravitational wave (GW) detectors. This paper proposes a low-frequency hierarchical cooperative impulse control strategy and a high-fidelity orbit optimization method to achieve a formation of GW detectors with high detection performance. The control strategy employs a hierarchical structure to divide the configuration control into position and shape layers. In the upper layer, the position layer, a state transition tensor method is employed to analyze the sensitivity and feasible range of the formation center position on the configuration stability. In the lower layer, the shape layer, a novel consistency protocol cooperatively uses the states of all individuals in the formation to determine the control expectations. The constraint on formation position is relaxed to reduce the number of impulses, achieving a low-frequency impulse control. The optimization method, characterized by a careful selection of the optimization variables and a design of adaptive model continuation from a low-fidelity model to a high-fidelity model, is proposed to reduce the problem-solving difficulty. The proposed strategy and method are applied to the Laser Interferometer Space Antenna (LISA) mission, and the results demonstrate that the configuration stability is effectively enhanced with several low-frequency impulses.